Problem: A function $f$ has domain $[0,2]$ and range $[0,1]$. (The notation $[a,b]$ denotes $\{x:a \le x \le b \}$.) Let
\[g(x) = 1 - f(x + 1).\]Then the domain of $g(x)$ is $[a,b],$ and the range of $g(x)$ is $[c,d].$  Enter the ordered quadruple $(a,b,c,d).$
Explanation: For $g(x) = 1 - f(x + 1)$ to be defined, we need
\[0 \le x + 1 \le 2,\]or $-1 \le x \le 1.$  As $y$ ranges over $0 \le y \le 1,$ $1 - y$ ranges from 1 to 0.  Hence, $(a,b,c,d) = \boxed{(-1,1,0,1)}.$